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Time Series Analysis

415 words - 2 pages

Time Series Analysis
Yt=observed value of the time series in time period t
TRt=the trend component or factorin time period t
SNt=the seasonal componentor factorin time period t
CLt=the cyclical componentor factorin time period t
IRt=the irregular componentor factorin time period t
7.1)
CL*IRCL=IR

a) SN1=1.191
TR1=240.5
CL1=null
IRt=null
SN2=1.521
TR2=260.4
CL2=0.998
IR2=0.990
SN3=0.804
TR3=280.4
CL3=0.994
IR3=0.986
SN4=0.484
TR4=300.3
...view middle of the document...

53+19.94(t)
c) Yt=trt*snt
Y17=220.53+19.9417*1.191=666.6
Y18=220.53+19.9418*1.521=881.6
Y19=220.53+19.9419*0.804=482.1
Y20=220.53+19.9420*0.484=299.9
d)
Yt=trt*snt*cl
We cannot see a definitive cycle and because the values of cl are close to 1. We do not take it into account.
Y21=220.53+19.9421*0.191=761.6
e)
Since there are just four years of data and most values are near 1 we cannot discern a well-defined cycle.
f)
Y21=220.53+19.9421*0.191=761.6
It agrees with the values computed in part c
g) Excel Spreadsheet
h)
Prediction intervals for the next 4 quarters t=17,18,19,20
t=17:654.094,679.542
t=18:869.038,894.542
t=19:469.107,494.556
t=20:286.977,312.426

8.1)
Smoothing equation
l0=t=1nYtn Which is the average of the first series values
lT=αyT+(1-α)lT-1
α:smoothing constant
Yt+1=lt
a)
l0=360.66
l1=0.1362+0.9360.66=360.80
l2=0.1381+0.9360.80=362.82
l3=0.1317+0.9362.82=358.23
b)
l4=0.1297+0.9358.23=352.11
Forecast error for τ=4: 297-358.23=-61.23
c)
l4=0.1297+0.9358.23=352.11

d)
Forecast error for τ=5: 399-352.11=46.89
8.3)
a)
PI Y28=354.54±1.9634.951+30.034=[282.62,426.45]
b)
YT+τT=lT
Y24+524=l24=348.63

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